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Circumference of a Circle

The perimeter of a circle is called the circumference of a circle.

But it is not easy to find the circumference of a circle because the boundary is not made of straight lines or edges. This problem of calculating the circumference of a circle has puzzled mathematicians for centuries. It was known in ancient Egypt that the distance around the boundary of a circle was directly linked to the length of its diameter.

This relationship, expressed as     circumference of circle

{Circumference (C)}/{Diameter (d)}~~=~~pi

results in a number pi (called pi) with a value of

pi  =  3.141 592 653 589 793 238 462 643 383 279 ….

This number continues forever without repetition and does not have a pattern that repeats. It is important to note that pi is an irrational number as it does not have an exact fraction or decimal value.


Over the centuries, many people have tried to express pi as a fraction. In ancient Egypt (around 1700 BC), 256/81 ~ 3.1605 was used to estimate pi. In ancient Greece, the great mathematician Archimedes (around 225 BC) stated that the value of pi lay between 310/71 and 31/7. The famous Chinese mathematician Tsu Ch’ung-chih (circa 470 AD) gave the value of pi as 355/113, which is accurate to 6 decimal places. In the 13th century, Fibonacci estimate the value as 864/275 ~ 3.14 8…

However, today the commonly used approximations for pi is 22/7 as a fraction, and 3.14 as a decimal.

If you are using a scientific calculator, the value of pi should be obtained by pressing the pi key, unless otherwise indicated.

pi is used in most calculations involving circles and cylinders.


Formula for circumference of a circle

As discussed above, pi~~=~~{Circumference (C)}/{Diameter (d)}

Rearranging this, we get the formula for circumference C = pi d

In other words, the circumference of a circle is obtained by multiplying pi and the diameter (d) of the circle.

This formula can be expressed in terms of the radius, r as:

C  =  pi d

=  pi~*2r (since d = 2r)

=  2pi r

circle with diameter d circle with radius r
C  =  pi d C  =  2pi r


Now let us look at a few examples:

1. What is the circumference of this circle? circle with diameter=14 cm

C  =  pi d

=  {22/7}~*~14

=  44 cm


2. Calculate the circumference of the circle, correct to 1 decimal place.     circle with radius=9 cm

C  =  2pi r

=  2~*~pi~*~9

=  2~*~3.14~*~9

=  56.5 cm

Note: In this example, the circumference could also be expressed as 18pi

We’ll look at calculating the area of a circle.